Problem: Gabriela is 5 times as old as Emily and is also 20 years older than Emily. How old is Emily?
We can use the given information to write down two equations that describe the ages of Gabriela and Emily. Let Gabriela's current age be $g$ and Emily's current age be $e$ $g = 5e$ $g = e + 20$ Now we have two independent equations, and we can solve for our two unknowns. Since we are looking for $e$ , and both of our equations have $g$ alone on one side, this is a convenient time to use elimination. Subtracting the second equation from the first equation, we get: $0 =$ $5e$ $-$ $ (e + 20)$ which combines the information about $e$ from both of our original equations. Solving for $e$ , we get: $4 e = 20$ $e = 5$.